相关论文: Pointed fusion systems of blocks

In this note, we prove that stable equivalences of Morita type between blocks of finite groups induce identification of certain quotient fusion systems under sone assumption. We also collect some related results for separable equivalences.

To any block idempotent $b$ of a group algebra $kG$ of a finite group $G$ over a field $k$ of characteristic $p>0$, Puig associated a fusion system and proved that it is saturated if the $k$-algebra $kC_G(P)e$ is split, where $(P,e)$ is a…

A pointed fusion category is a rigid tensor category with finitely many isomorphism classes of simple objects which moreover are invertible. Two tensor categories $C$ and $D$ are weakly Morita equivalent if there exists an indecomposable…

This article is dedicated to the proof of the following theorem. Let G be a finite group, p be a prime number, and e be a p-block of G. Assume that the centraliser C_G(P) of an e-subpair (P,e_P) "strongly" controls the fusion of the block…

We introduce block pro-fusion systems for blocks of profinite groups, prove a profinite version of Puig's structure theorem for nilpotent blocks, and use it to show that there is only one Morita equivalence class of blocks having the…

In this paper we give a complete classification of pointed fusion categories over $\mathbb{C}$ of global dimension 8. We first classify the equivalence classes of pointed fusion categories of dimension 8, and then we proceed to determine…

We give a complete classification of pointed fusion categories over $\mathbb{C}$ of global dimension $p^3$ for $p$ any odd prime. We proceed to classify the equivalence classes of pointed fusion categories of dimension $p^3$ and we…

It was shown by Ostrik (2003) and Natale (2017) that a collection of twisted group algebras in a pointed fusion category serve as explicit Morita equivalence class representatives of indecomposable, separable algebras in such categories. We…

We prove the conjecture that exotic and block-exotic fusion systems coincide holds for all fusion systems on exceptional $p$-groups of maximal nilpotency class, where $p \geq 5$. This is done by considering a family of exotic fusion systems…

Our work explores fusions, the multidimensional counterparts of mean-preserving contractions and their extreme and exposed points. We reveal an elegant geometric/combinatorial structure for these objects. Of particular note is the…

In this article, we consider the control of fusion in fusion systems, proving three previously known, non-trivial results in a new, largely elementary way. We then reprove a result of Aschbacher, that the product of two strongly closed…

We say that a fusion system is the composition product of two subsystems if every morphism can be factored as a morphism in one fusion system followed by a morphism in the other. We establish a relationship between the characteristic…

We classify principal blocks of finite groups with semidihedral defect groups up to splendid Morita equivalence. This completes the classification of all principal $2$-blocks of tame representation type up to splendid Morita equivalence and…

Given a saturated fusion system $\mathcal{F}$ over a $2$-group $S$, we prove that $S$ is abelian provided any element of $S$ is $\mathcal{F}$-conjugate to an element of $Z(S)$. This generalizes a Theorem of Camina--Herzog, leading to a…

We classify pointed fusion categories C(G, $\omega$) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2 3 , 2 4 and 3 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their…

We discuss representations of finite groups having a common central $p$-subgroup $Z$, where $p$ is a prime number. For the principal $p$-blocks, we give a method of constructing a relative $Z$-stable equivalence of Morita type, which is a…

Fusion rules in turbulence specify the analytic structure of many-point correlation functions of the turbulent field when a group of coordinates coalesce. We show that the existence of flux equilibrium in fully developed turbulent systems…

We show that, given an almost-source algebra $A$ of a $p$-block of a finite group $G$, then the unit group of $A$ contains a basis stabilized by the left and right multiplicative action of the defect group if and only if, in a sense to be…

For a $p$-permutation equivalence between two block algebras of finite groups, we introduce new square diagrams that link the $p$-permutation equivalence via the Brauer construction to local equivalences between stabilizers of corresponding…

A pointed $p$-group is a pointed group $P_\gamma$ such that $P$ is a $p$-group. We parameterize the pointed $p$-groups on a group algebra or on a block algebra of a group algebra. The parameterization involves $p$-subgroups and irreducible…